The transient and steady-state characteristics of a two-stage transfer line production system subject to inter-stage inspection and initial buffer are studied. The initial buffer has finite capacity N, and when the buffer size reaches a level n, a replenishment order for a size (N - n) is placed. The first stage of production is never starved until the buffer level reaches zero, and the second stage of production is never blocked. A stochastic model is developed to describe the system, and analytical expressions for percentage utilization, idle time and blocked duration, with arbitary distributions of processing times at both stages of production and exponential arrival pattern to the buffer upon ordering, have been obtained by using a state-space method and regeneration point technique.